A387555 a(n) = (1/2) * Sum_{k=0..floor(n/3)} 2^(n-k) * binomial(2*k+2,2*n-6*k+1).

1, 0, 0, 8, 16, 0, 48, 320, 192, 256, 3584, 7168, 3328, 30720, 129024, 129024, 245760, 1622016, 3272704, 3293184, 16596992, 56360960, 74776576, 166985728, 752156672, 1552941056, 2268069888, 8638693376, 25806503936, 41498443776, 99265544192, 357275009024

Offset: 0

Author

Seiichi Manyama, Sep 02 2025

Keywords

• nonn
• easy
• new

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1500
• Index entries for linear recurrences with constant coefficients, signature (0,0,8,16,0,-16,64,-64).

Crossrefs

Cf. A387484.

Programs

Magma

[&+[2^(n-k) * Binomial(2*k+2, 2*n-6*k+1)/2: k in [0..Floor(n/3)]]: n in [0..40]]; // Vincenzo Librandi, Sep 02 2025

Mathematica

Table[Sum[2^(n-k)*Binomial[2*k+2, 2*n-6*k+1]/2,{k,0,Floor[n/3]}],{n,0,40}] (* Vincenzo Librandi, Sep 02 2025 *)

PARI

a(n) = sum(k=0, n\3, 2^(n-k)*binomial(2*k+2, 2*n-6*k+1))/2;

Formula

G.f.: B(x)^2, where B(x) is the g.f. of A387484.

G.f.: 1/((1-4*x^3-8*x^4)^2 - 128*x^7).

a(n) = 8*a(n-3) + 16*a(n-4) - 16*a(n-6) + 64*a(n-7) - 64*a(n-8).